= Solution
The <Rayleigh criterion> declares two equal incoherent point images just resolved when the central maximum of one lies at the first minimum of the other's <point spread function>. For a single rectangular slit, the first minimum occurs at $w\sin\theta_1=\lambda$. Thus
$$
\boxed{\Delta\theta_R=\sin^{-1}(\lambda/w)\simeq\lambda/w.}
$$
This is a resolution in the direction across the slit width, and the last approximation requires $\lambda\ll w$. The central maximum's full width between its two first minima is approximately $2\lambda/w$; it is not the <Rayleigh criterion>'s separation. Two coherent sources can interfere with one another, so a resolution statement for them also needs their relative <phase>.
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